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The dynamics of the transitional flow over a backward-facing step

Published online by Cambridge University Press:  06 March 2009

F. SCHÄFER ,
M. BREUER  and
F. DURST
F. SCHÄFER
Affiliation:
Institute of Fluid Mechanics, University of Erlangen–Nuremberg, Cauerstrasse 4, D-91058 Erlangen, Germany
M. BREUER*
Affiliation:
Institute of Fluid Mechanics, University of Erlangen–Nuremberg, Cauerstrasse 4, D-91058 Erlangen, Germany
F. DURST
Affiliation:
Institute of Fluid Mechanics, University of Erlangen–Nuremberg, Cauerstrasse 4, D-91058 Erlangen, Germany
*
†Present address for correspondence: Department of Fluid Mechanics, Institute of Mechanics, Helmut-Schmidt-University Hamburg, Holstenhofweg 85, D-22043 Hamburg, Germany. Email: breuer@hsu-hh.de
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Abstract

The internal flow over a backward-facing step in the transitional regime (ReD = 6000) was studied based on direct numerical simulations. The predictions were carried out with the help of a finite-volume Navier–Stokes solver equipped with a co-visualization facility which allows one to investigate the flow dynamics at high temporal resolution. First, grid-induced oscillations were precluded by a careful grid design. Second, the strong influence of the velocity profile approaching the step was studied and outlined. The main objective, however, was to provide a comprehensive insight into the dynamic flow behaviour, especially oscillations of the reattachment length of the primary recirculation region. The origin of this well-known flapping behaviour of the reattachment line is not yet completely understood. In the present work, the mechanisms leading to the oscillations of the reattachment length were extensively investigated by analysing the time-dependent flow. Besides the oscillations of the primary recirculation region, oscillations of the separation and the reattachment line of the secondary recirculation bubble at the upper channel wall were also observed. The results clearly show that in the present flow case the flapping of the primary reattachment and the secondary separation line is due to vortical structures in the unstable shear layers between the main flow and the recirculation bubbles. Vortices emerging in the shear layers and sweeping downstream convectively induce small zones of backward-flowing fluid at the channel walls while passing the recirculation regions. In the case of the primary recirculation region, the rotational movement of the shear-layer vortices impinging on the lower channel wall was found to cause zones of negative fluid velocity at the end of the recirculation bubble and thus flapping of the reattachment line. In contrast, in the case of the secondary recirculation region, the shear-layer vortices moved away from the upper channel wall so that their rotational movement did not reach the boundary. In this case, the pressure gradients originating from local pressure minima located in the shear-layer vortices were identified as being responsible for the oscillations of the separation line at the upper channel wall. While moving downstream with the shear-layer vortices, the pressure gradients were found to influence the top boundary of the channel and create alternating zones of forward- and backward-flowing fluid along the wall. All of these unsteady processes can best be seen from animations which are provided on the Journal of Fluid Mechanics website: journals.cambridge.org/FLM.

JFM classification

Wakes/Jets: Separated flows Wakes/Jets: Shear layers Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 623 , 25 March 2009 , pp. 85 - 119
Copyright
Copyright © Cambridge University Press 2009

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References

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Schafer et al. supplementary movie

Movie 1. Iso-surface of zero streamwise flow velocity, separating regions with negative and positive streamwise velocity. Temporal fluctuations of the primary reattachment and the secondary separation line are found.

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Video 10.3 MB

Schafer et al. supplementary movie

Movie 2. Iso-surface of low fluid pressure, showing the development of flow structures in the shear layers between the main flow and the two recirculation regions.

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Video 10.3 MB

Schafer et al. supplementary movie

Movie 3. Iso-surface of zero streamwise flow velocity (red) and iso-surface of low fluid pressure (yellow). The interaction between the flow structures in the shear layers and the recirculation regions can be observed.

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Video 10.2 MB

Schafer et al. supplementary movie

Movie 4. Streaklines initiated at particle source region 1 just in front of the step (colour coding according to pressure). Vortex structures are developing in the unstable shear layers.

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Video 9.5 MB

Schafer et al. supplementary movie

Movie 5. Streaklines initiated at particle source region 2 between the step and the primary reattachment zone (colour coding according to pressure). The roll-up process in the early phase of vortex development is shown more clearly.

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Video 10.3 MB

Schafer et al. supplementary movie

Movie 6. Streaklines initiated at particle source region 2 between the step and the primary reattachment zone (colour coding according to streamwise velocity, particles with negative streamwise velocity are coloured blue). The movie shows that there is a relation between the lower shear layer vortices and the regions with negative streamwise velocity at the bottom wall downstream of the primary reattachment line. These regions are swept downstream convectively together with the vortices.

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Video 10.5 MB

Schafer et al. supplementary movie

Movie 7. Iso-surfaces of zero streamwise flow velocity and streaklines initiated at particle source region 2 (colour coding of streaklines according to streamwise velocity, particles with negative streamwise velocity are coloured blue). The relation between the shear layer vortices and the regions with negative streamwise velocity at the bottom and at the top wall is clearly shown.

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Video 10.3 MB

Schafer et al. supplementary movie

Movie 8. Iso-surfaces of zero streamwise flow velocity and streaklines initiated at particle source region 2 (colour coding of streaklines according to pressure). In order to reveal the rotating vortex motion more clearly, particles are displayed as tangents to the local flow direction relative to the average streamwise convective vortex motion.

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Video 9.2 MB

Schafer et al. supplementary movie

Movie 9. Streaklines initiated at particle source regions 3 and 4, located next to the end of the primary and the secondary recirculation region, respectively (colour coding according to pressure). A pulsating movement of particles along the upper wall within the secondary recirculation region is found. At the same time, regions of high and low pressure are moving through the secondary recirculation region. The low pressure regions are associated to vortices in the upper shear layer.

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Video 8 MB

Schafer et al. supplementary movie

Movie 10. Streaklines initiated at particle source region 3, located next to the end of the primary recirculation region (colour coding according to seed position). Streak-like structures are found along the bottom wall within the primary recirculation region. Moreover, the interaction between the lower shear layer vortices and the primary recirculation bubble can be seen.

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Video 7.9 MB